How to learn Kindergarten: Mathematics

Georgia academic standards: Mathematics, Kindergarten

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1. Geometric & Spatial Reasoning · Identify, describe, and compare basic shapes encountered in the environment, and form two-dimensional shapes and three-dimensional figures.

1. 2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
2. Combining Simple Shapes: Compose simple shapes to form larger shapes (e.g. two triangles make a rectangle)
3. Composing Shapes: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape
4. Positional Language: Describe the position of objects using terms such as above, below, beside, in front of, behind, next to
5. 3-D shapes (age 5+): Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes

2. Measurement & Data Reasoning · Observe, describe, and compare the physical and measurable attributes of objects and analyze graphical displays of data to answer relevant questions.

1. Measurable Attributes of Objects: Describe and identify measurable attributes of objects such as length, height, weight, and capacity; use comparative language (longer, shorter, heavier, lighter, more, less)
2. Sorting into categories: Classify objects into given categories, count the number in each category, and sort the categories by count

3. Patterning & Algebraic Reasoning · Explain, extend, and create repeating patterns with a repetition, not exceeding 4 and describe patterns involving the passage of time.

1. Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences

4. Numerical Reasoning · Explain the concepts of addition, subtraction, and equality and use these concepts to solve real-life problems within 10.

1. Representing Addition and Subtraction: Represent addition and subtraction using objects, drawings, and mental images
2. Addition and subtraction word problems: Solve addition and subtraction word problems within 10 using objects or drawings
3. Finding a missing number in addition: Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)
4. Numbers up to 10 into pairs: Decompose numbers up to 10 into pairs in more than one way (part-part-whole)

5. Numerical Reasoning · Identify, write, represent, and compare numbers up to 20.

1. Comparing groups: more or fewer: Compare two groups of objects to determine which has more, fewer, or whether they are equal, using matching and counting strategies
2. Counting objects to 20: Count a set of objects to answer 'how many?' for sets up to 20 (arranged in lines, arrays, circles, or scattered)
3. Reading and writing numbers to 20: Read and write numerals from 0 to 20

6. Numerical Reasoning · Use place value understanding to compose and decompose numbers from 11–19.

1. The teen numbers: Understand that the teen numbers (11–19) are composed of ten ones and some further ones (early place value)

7. Numerical Reasoning · Use count sequences within 100 to count forward and backward in sequence.

1. Counting forwards and backwards: Count forwards and backwards in steps of 3 from 0
2. Rote counting to 100: Rote count forwards and backwards from 0 to 100, beginning from 0, 1, or any given number, by ones

8. Numerical Reasoning · Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the last number counted represents the total quantity in a set)

1. Connecting Representations: Move between real-world situations, drawings, and number sentences, explaining how each representation connects to the others (quantitative reasoning)
2. How Many in Total?: Cardinality principle: the last number said when counting a set tells how many objects are in the set, regardless of arrangement or order counted
3. One More Each Time: Each successive counting number represents a quantity that is one larger than the previous number

9. Mathematical Practices · Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective

1. Explaining Mathematical Reasoning: With teacher prompting, explain and justify mathematical reasoning using drawings, number sentences, or words
2. Making Sense of Problems: Make sense of a problem by identifying what is being asked, choosing concrete objects or pictures to represent the situation, and explaining a pathway to the solution
3. Precise Maths Communication: Communicate with mathematical precision: use correct vocabulary, specify units, and use symbols accurately